On tangent cones to Schubert varieties in type E

We consider tangent cones to Schubert subvarieties of the flag variety G/B, where B is a Borel subgroup of a reductive complex algebraic group G of type E6, E7 or E8. We prove that if w1 and w2 form a good pair of involutions in the Weyl group W of G then the tangent cones Cw1 and Cw2 to the corresponding Schubert subvarieties of G/B do not coincide as subschemes of the tangent space to G/B at the neutral point.

Measuring the Consistency of Quantitative and Qualitative Information in Financial Reports: A Design Science Approach

ABSTRACT This study uses a design science approach to examine the consistency between quantitative financial ratios and qualitative narrative disclosures in the annual reports. To extract information on the tone of unstructured qualitative textual data, we first use the term frequency/inverse document frequency (TFIDF) text mining technique to classify each company's narrative disclosure as either “Positive” or “Negative.” For the quantitative information, we use the K-means method to cluster each company's financial performance data into “Good” or “Poor” groups. Consistency is said to occur when the textual and numerical data form either a “Positive-Good” pair or a “Negative-Poor” pair. The design model is presented in a stepwise fashion and therefore is transparent for evaluation and validation. Our evaluation process demonstrates the feasibility of the design model. The evaluation was conducted using listed semiconductor companies in countries with different levels of market development. The results show that U.S. firms are less likely to exaggerate in their narrative disclosures and are more likely to understate their performance in MD&As compared to companies in other markets such as China and Taiwan.

Study on Composite Materials Used in the Tennis Racket

In many sports, tennis occupies an important position. For a tennis player, it is an important factor in a good pair of tennis to win the game. The composite materials in the production process in tennis racket are studies in this paper. Analyzed and demonstrated several ways from its function and structure, process performance, process and process analysis. Finally, the production process of the racket will be detailed study, and then a conclusion will be get that is composite material has important practical value in the production of a tennis racket.

Comparison and Application of Metrics That Define the Components Modularity in Complex Products

As the content and variety of technology increases in automobiles, the complexity of the system increases as well. Decomposing systems into modules is one of the ways to manage and reduce system complexity. This paper surveys and compares a number of state-of-art components modularity metrics, using 8 sample test systems. The metrics include Whitney Index (WI), Change Cost (CC), Singular value Modularity Index (SMI), Visibility-Dependency (VD) plot, and social network centrality measures (degree, distance, bridging). The investigation reveals that WI and CC form a good pair of metrics that can be used to assess component modularity of a system. The social network centrality metrics are useful in identifying areas of architecture improvements for a system. These metrics were further applied to two actual vehicle embedded software systems. The first system is going through an architecture transformation. The metrics from the old system revealed the need for the improvements. The second system was recently architected, and the metrics values showed the quality of the architecture as well as areas for further improvements.

Increase of Stress Intensity near Free-Edge of Elastic-Creeping Bi-Material Interface under a Sustained Load

The transition from SSC to LSC ahead of a crack tip (notch root) or an ordinary interface edge (bad pair) causes stress relaxation and the decrease of stress intensity in general. However, the good pair bi-material and the bad pair bi-material with weak elastic stress singularity in this study show the inverse phenomenon under the transition. The results indicate that the stress near the interface edges of both cases, which have no or low stress singularity at the loading instant, increases and brings about the stress concentration during the transition. In addition, the creep strain distribution in the early stage is different from that occurred in the transition of an ordinary interface edge (bad pair) or a crack tip (notch root).